{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practical Statistics for Data Scientists (R)\n",
    "# Chapter 2. Data and Sampling Distributions\n",
    "> (c) 2019 Peter C. Bruce, Andrew Bruce, Peter Gedeck"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import required R packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:49:57.464576Z",
     "iopub.status.busy": "2022-04-26T11:49:57.461380Z",
     "iopub.status.idle": "2022-04-26T11:49:57.796267Z",
     "shell.execute_reply": "2022-04-26T11:49:57.794733Z"
    }
   },
   "outputs": [],
   "source": [
    "library(boot)\n",
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define paths to data sets. If you don't keep your data in the same directory as the code, adapt the path names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:49:57.824912Z",
     "iopub.status.busy": "2022-04-26T11:49:57.799579Z",
     "iopub.status.idle": "2022-04-26T11:50:05.388599Z",
     "shell.execute_reply": "2022-04-26T11:50:05.387161Z"
    }
   },
   "outputs": [],
   "source": [
    "PSDS_PATH <- file.path(dirname(dirname(getwd())))\n",
    "\n",
    "loans_income <- read.csv(file.path(PSDS_PATH, 'data', 'loans_income.csv'))\n",
    "loans_income <- loans_income[, 1]   # convert data frame to vector\n",
    "sp500_px <- read.csv(file.path(PSDS_PATH, 'data', 'sp500_data.csv.gz'), row.names=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 2.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:05.392663Z",
     "iopub.status.busy": "2022-04-26T11:50:05.391658Z",
     "iopub.status.idle": "2022-04-26T11:50:05.475483Z",
     "shell.execute_reply": "2022-04-26T11:50:05.474248Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>null device:</strong> 1"
      ],
      "text/latex": [
       "\\textbf{null device:} 1"
      ],
      "text/markdown": [
       "**null device:** 1"
      ],
      "text/plain": [
       "null device \n",
       "          1 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<strong>null device:</strong> 1"
      ],
      "text/latex": [
       "\\textbf{null device:} 1"
      ],
      "text/markdown": [
       "**null device:** 1"
      ],
      "text/plain": [
       "null device \n",
       "          1 "
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     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
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A5y+uk/z84+IPHRUlu39enTafv2KdYZ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\nF0FNK6ymtRW5AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(from=-3, to=3, length=300)\n",
    "gauss <- dnorm(x)\n",
    "\n",
    "    par(mar=c(3, 3, 0, 0)+.1)\n",
    "    plot(x, gauss, type='l', col='blue', xlab='', ylab='', axes=FALSE)\n",
    "    polygon(x, gauss, col='blue')\n",
    "dev.off()\n",
    "\n",
    "    norm_samp <- rnorm(100)\n",
    "    par(mar=c(3, 3, 0, 0)+.1)\n",
    "    hist(norm_samp, axes=FALSE, col='red', main='')\n",
    "dev.off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sampling Distribution of a Statistic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:05.481226Z",
     "iopub.status.busy": "2022-04-26T11:50:05.479967Z",
     "iopub.status.idle": "2022-04-26T11:50:05.898450Z",
     "shell.execute_reply": "2022-04-26T11:50:05.896779Z"
    }
   },
   "outputs": [],
   "source": [
    "# take a simple random sample\n",
    "samp_data <- data.frame(income=sample(loans_income, 1000), \n",
    "                        type='data_dist')\n",
    "\n",
    "# take a sample of means of 5 values\n",
    "samp_mean_05 <- data.frame(\n",
    "  income = tapply(sample(loans_income, 1000*5), \n",
    "                  rep(1:1000, rep(5, 1000)), FUN=mean),\n",
    "  type = 'mean_of_5')\n",
    "\n",
    "# take a sample of means of 20 values\n",
    "samp_mean_20 <- data.frame(\n",
    "  income = tapply(sample(loans_income, 1000*20), \n",
    "                  rep(1:1000, rep(20, 1000)), FUN=mean),\n",
    "  type = 'mean_of_20')\n",
    "\n",
    "# bind the data.frames and convert type to a factor\n",
    "income <- rbind(samp_data, samp_mean_05, samp_mean_20)\n",
    "income$type <- factor(income$type, \n",
    "                     levels=c('data_dist', 'mean_of_5', 'mean_of_20'),\n",
    "                     labels=c('Data', 'Mean of 5', 'Mean of 20'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:05.903762Z",
     "iopub.status.busy": "2022-04-26T11:50:05.902404Z",
     "iopub.status.idle": "2022-04-26T11:50:06.782149Z",
     "shell.execute_reply": "2022-04-26T11:50:06.780698Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KLyIuxvDJ+zY94DSECa3UXY3xg+Z8e8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\nQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(income, aes(x=income)) +\n",
    "  geom_histogram(bins=40) +\n",
    "  facet_grid(type ~ .)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Bootstrap\n",
    "As the calculation uses random samples, results will vary between runs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:06.787032Z",
     "iopub.status.busy": "2022-04-26T11:50:06.786075Z",
     "iopub.status.idle": "2022-04-26T11:50:11.249584Z",
     "shell.execute_reply": "2022-04-26T11:50:11.248268Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "ORDINARY NONPARAMETRIC BOOTSTRAP\n",
       "\n",
       "\n",
       "Call:\n",
       "boot(data = loans_income, statistic = stat_fun, R = 1000)\n",
       "\n",
       "\n",
       "Bootstrap Statistics :\n",
       "    original   bias    std. error\n",
       "t1*    62000 -75.8725     220.336"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stat_fun <- function(x, idx) median(x[idx])\n",
    "boot_obj <- boot(loans_income, R=1000, statistic=stat_fun)\n",
    "\n",
    "boot_obj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Confidence Intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:11.254466Z",
     "iopub.status.busy": "2022-04-26T11:50:11.253349Z",
     "iopub.status.idle": "2022-04-26T11:50:11.566362Z",
     "shell.execute_reply": "2022-04-26T11:50:11.565256Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 2 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>ci</th><th scope=col>y</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>51643.09</td><td> 9</td></tr>\n",
       "\t<tr><td>65262.95</td><td>11</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 2 × 2\n",
       "\\begin{tabular}{ll}\n",
       " ci & y\\\\\n",
       " <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 51643.09 &  9\\\\\n",
       "\t 65262.95 & 11\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 2 × 2\n",
       "\n",
       "| ci &lt;dbl&gt; | y &lt;dbl&gt; |\n",
       "|---|---|\n",
       "| 51643.09 |  9 |\n",
       "| 65262.95 | 11 |\n",
       "\n"
      ],
      "text/plain": [
       "  ci       y \n",
       "1 51643.09  9\n",
       "2 65262.95 11"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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U/G9BGSACGhT8b0EZIAIYX3qUs3h74LszKmj5AECCk8PpA1ICR1hKQlY/oISYCQ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\nhAQ4QEiAA/8fp3lf+aVtfqQAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# R version for figure 2-9 not available\n",
    "set.seed(5)\n",
    "set.seed(7)\n",
    "sample20 <- sample(loans_income, 20)\n",
    "sampleMean <- mean(sample20)\n",
    "\n",
    "stat_fun <- function(x, idx) mean(x[idx])\n",
    "boot_obj <- boot(sample20, R=500, statistic=stat_fun)\n",
    "boot_ci <- boot.ci(boot_obj, conf=0.9, type='basic')\n",
    "X <- data.frame(mean=boot_obj$t)\n",
    "ci90 <- boot_ci$basic[4:5]\n",
    "ci <- data.frame(ci=ci90, y=c(9, 11))\n",
    "# ci <- boot_ci$basic[4:5]\n",
    "ci\n",
    "ggplot(X, aes(x=mean)) +\n",
    "    geom_histogram(bins=40, fill='#AAAAAA') +\n",
    "    geom_vline(xintercept=sampleMean, linetype=2) +\n",
    "    geom_path(aes(x=ci, y=10), data=ci, size=2) +\n",
    "    geom_path(aes(x=ci90[1], y=y), data=ci, size=2) +\n",
    "    geom_path(aes(x=ci90[2], y=y), data=ci, size=2) +\n",
    "    geom_text(aes(x=sampleMean, y=20, label='Sample mean'), size=6) +\n",
    "    geom_text(aes(x=sampleMean, y=8, label='90% interval'), size=6) +\n",
    "    theme_bw() + \n",
    "    labs(x='', y='Counts')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Normal Distribution\n",
    "## Standard Normal and QQ-Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:11.571069Z",
     "iopub.status.busy": "2022-04-26T11:50:11.570102Z",
     "iopub.status.idle": "2022-04-26T11:50:11.634567Z",
     "shell.execute_reply": "2022-04-26T11:50:11.632673Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xNASC4g7+hhw/+en8ibeQS4y/5YI/P7Q7zK/f73Hlc2iZN4mc45ICTnd7PqGtVt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\ngJAAGPh/LIRKwr63uhEAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm_samp <- rnorm(100)\n",
    "qqnorm(norm_samp, main='', xlab='Quantile of normal distribution', ylab='z-score')\n",
    "abline(a=0, b=1, col='grey')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Long-Tailed Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:11.638838Z",
     "iopub.status.busy": "2022-04-26T11:50:11.637772Z",
     "iopub.status.idle": "2022-04-26T11:50:11.736013Z",
     "shell.execute_reply": "2022-04-26T11:50:11.734237Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ee9lJcz6XQjVVpDmisI29m5dEUbmslvUAjJdK4K7ugFxcXk6UYWzEh7SD2q/cw2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\ncICQADj4fygFWUhPXv8wAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “Normal Q-Q Plot”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nflx <- sp500_px[,'NFLX']\n",
    "nflx <- diff(log(nflx[nflx>0]))\n",
    "qqnorm(nflx)\n",
    "abline(a=0, b=1, col='grey')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binomial Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:11.740553Z",
     "iopub.status.busy": "2022-04-26T11:50:11.739371Z",
     "iopub.status.idle": "2022-04-26T11:50:11.751944Z",
     "shell.execute_reply": "2022-04-26T11:50:11.750436Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0729"
      ],
      "text/latex": [
       "0.0729"
      ],
      "text/markdown": [
       "0.0729"
      ],
      "text/plain": [
       "[1] 0.0729"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dbinom(x=2, size=5, p=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:11.756561Z",
     "iopub.status.busy": "2022-04-26T11:50:11.755423Z",
     "iopub.status.idle": "2022-04-26T11:50:11.767364Z",
     "shell.execute_reply": "2022-04-26T11:50:11.765950Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.99144"
      ],
      "text/latex": [
       "0.99144"
      ],
      "text/markdown": [
       "0.99144"
      ],
      "text/plain": [
       "[1] 0.99144"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pbinom(2, 5, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:11.772205Z",
     "iopub.status.busy": "2022-04-26T11:50:11.771070Z",
     "iopub.status.idle": "2022-04-26T11:50:11.783149Z",
     "shell.execute_reply": "2022-04-26T11:50:11.781830Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0175879466057216"
      ],
      "text/latex": [
       "0.0175879466057216"
      ],
      "text/markdown": [
       "0.0175879466057216"
      ],
      "text/plain": [
       "[1] 0.01758795"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dbinom(x=0, size=200, p=0.02)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Poisson and Related Distribution\n",
    "## Poisson Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:11.788071Z",
     "iopub.status.busy": "2022-04-26T11:50:11.786907Z",
     "iopub.status.idle": "2022-04-26T11:50:11.799099Z",
     "shell.execute_reply": "2022-04-26T11:50:11.797852Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1</li><li>2</li><li>1</li><li>3</li><li>2</li><li>2</li><li>2</li><li>5</li><li>4</li><li>1</li><li>2</li><li>3</li><li>2</li><li>6</li><li>1</li><li>5</li><li>6</li><li>2</li><li>3</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>3</li><li>4</li><li>3</li><li>0</li><li>2</li><li>6</li><li>5</li><li>2</li><li>4</li><li>1</li><li>0</li><li>2</li><li>0</li><li>2</li><li>3</li><li>5</li><li>3</li><li>1</li><li>4</li><li>4</li><li>4</li><li>0</li><li>3</li><li>3</li><li>2</li><li>2</li><li>0</li><li>2</li><li>2</li><li>4</li><li>1</li><li>1</li><li>3</li><li>3</li><li>3</li><li>4</li><li>2</li><li>3</li><li>3</li><li>1</li><li>1</li><li>2</li><li>1</li><li>2</li><li>3</li><li>1</li><li>4</li><li>0</li><li>3</li><li>1</li><li>2</li><li>0</li><li>3</li><li>2</li><li>3</li><li>0</li><li>3</li><li>1</li><li>2</li><li>2</li><li>4</li><li>0</li><li>2</li><li>1</li><li>2</li><li>3</li><li>0</li><li>1</li><li>3</li><li>2</li><li>2</li><li>1</li><li>4</li><li>0</li><li>3</li><li>6</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 5\n",
       "\\item 4\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 6\n",
       "\\item 1\n",
       "\\item 5\n",
       "\\item 6\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 3\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 6\n",
       "\\item 5\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 1\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 5\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 4\n",
       "\\item 4\n",
       "\\item 4\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 4\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 0\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 4\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 1\n",
       "4. 3\n",
       "5. 2\n",
       "6. 2\n",
       "7. 2\n",
       "8. 5\n",
       "9. 4\n",
       "10. 1\n",
       "11. 2\n",
       "12. 3\n",
       "13. 2\n",
       "14. 6\n",
       "15. 1\n",
       "16. 5\n",
       "17. 6\n",
       "18. 2\n",
       "19. 3\n",
       "20. 1\n",
       "21. 1\n",
       "22. 1\n",
       "23. 1\n",
       "24. 1\n",
       "25. 3\n",
       "26. 4\n",
       "27. 3\n",
       "28. 0\n",
       "29. 2\n",
       "30. 6\n",
       "31. 5\n",
       "32. 2\n",
       "33. 4\n",
       "34. 1\n",
       "35. 0\n",
       "36. 2\n",
       "37. 0\n",
       "38. 2\n",
       "39. 3\n",
       "40. 5\n",
       "41. 3\n",
       "42. 1\n",
       "43. 4\n",
       "44. 4\n",
       "45. 4\n",
       "46. 0\n",
       "47. 3\n",
       "48. 3\n",
       "49. 2\n",
       "50. 2\n",
       "51. 0\n",
       "52. 2\n",
       "53. 2\n",
       "54. 4\n",
       "55. 1\n",
       "56. 1\n",
       "57. 3\n",
       "58. 3\n",
       "59. 3\n",
       "60. 4\n",
       "61. 2\n",
       "62. 3\n",
       "63. 3\n",
       "64. 1\n",
       "65. 1\n",
       "66. 2\n",
       "67. 1\n",
       "68. 2\n",
       "69. 3\n",
       "70. 1\n",
       "71. 4\n",
       "72. 0\n",
       "73. 3\n",
       "74. 1\n",
       "75. 2\n",
       "76. 0\n",
       "77. 3\n",
       "78. 2\n",
       "79. 3\n",
       "80. 0\n",
       "81. 3\n",
       "82. 1\n",
       "83. 2\n",
       "84. 2\n",
       "85. 4\n",
       "86. 0\n",
       "87. 2\n",
       "88. 1\n",
       "89. 2\n",
       "90. 3\n",
       "91. 0\n",
       "92. 1\n",
       "93. 3\n",
       "94. 2\n",
       "95. 2\n",
       "96. 1\n",
       "97. 4\n",
       "98. 0\n",
       "99. 3\n",
       "100. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  [1] 1 2 1 3 2 2 2 5 4 1 2 3 2 6 1 5 6 2 3 1 1 1 1 1 3 4 3 0 2 6 5 2 4 1 0 2 0\n",
       " [38] 2 3 5 3 1 4 4 4 0 3 3 2 2 0 2 2 4 1 1 3 3 3 4 2 3 3 1 1 2 1 2 3 1 4 0 3 1\n",
       " [75] 2 0 3 2 3 0 3 1 2 2 4 0 2 1 2 3 0 1 3 2 2 1 4 0 3 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rpois(100, lambda=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exponential Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:11.803939Z",
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     "iopub.status.idle": "2022-04-26T11:50:11.815844Z",
     "shell.execute_reply": "2022-04-26T11:50:11.814553Z"
    }
   },
   "outputs": [
    {
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       "1. 6.6387056976319\n",
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       "36. 6.89840606392777\n",
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       "42. 10.9372709208196\n",
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       "61. 1.62813091390937\n",
       "62. 24.5761018324841\n",
       "63. 16.3374472028556\n",
       "64. 7.1010031654349\n",
       "65. 14.9024343879204\n",
       "66. 3.73627926008094\n",
       "67. 8.33818527665312\n",
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       "69. 9.61141072171641\n",
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       "71. 0.56829016949424\n",
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       "74. 11.7490146582233\n",
       "75. 3.95642243770367\n",
       "76. 2.44337729178369\n",
       "77. 9.85450135501933\n",
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       "79. 2.37537440145388\n",
       "80. 13.8170197320389\n",
       "81. 3.08518774704097\n",
       "82. 1.72244070330635\n",
       "83. 0.445838205571774\n",
       "84. 3.26657653786242\n",
       "85. 4.10568973965607\n",
       "86. 1.33629720053316\n",
       "87. 4.05508079079396\n",
       "88. 1.76590585149825\n",
       "89. 3.5914235193441\n",
       "90. 2.463207191322\n",
       "91. 0.0122641150969449\n",
       "92. 3.26816772576421\n",
       "93. 0.385862767880727\n",
       "94. 3.17886889711023\n",
       "95. 0.920671530423423\n",
       "96. 1.34112713625655\n",
       "97. 0.0603274325840175\n",
       "98. 2.97972794855013\n",
       "99. 3.78438647349781\n",
       "100. 0.993724381551147\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  [1]  6.638705698  0.006711071 15.878587439  6.385282642  8.689187718\n",
       "  [6]  0.274932847  1.060285215  6.015904303  0.093875017  6.455080602\n",
       " [11]  5.107568993  0.109575669  1.765047924  4.227557843  2.735554227\n",
       " [16]  2.997726241 10.191077841  4.240468833  5.387811716  1.497157135\n",
       " [21]  7.579095225  5.562681489  0.486764224  6.090781335  6.687533734\n",
       " [26] 11.269287234  0.240654313  0.935246479  0.237767026  2.176883069\n",
       " [31]  4.110882086  5.987012894  3.275767015  2.445181824  2.651181775\n",
       " [36]  6.898406064 19.070931960  4.248119792  0.343186936 12.450818987\n",
       " [41]  2.647791156 10.937270921  0.721764060  2.244586736  3.630282255\n",
       " [46]  6.024240218  6.942348827  3.908220823  1.472034554  3.390782559\n",
       " [51]  2.439800855 37.597482109  4.775333837 11.167763983  8.946549366\n",
       " [56]  7.299376037 12.101185163  3.056247963  4.740315424  4.895523689\n",
       " [61]  1.628130914 24.576101832 16.337447203  7.101003165 14.902434388\n",
       " [66]  3.736279260  8.338185277  7.306550126  9.611410722  5.024689697\n",
       " [71]  0.568290169  2.569636486  2.460176537 11.749014658  3.956422438\n",
       " [76]  2.443377292  9.854501355  6.621408963  2.375374401 13.817019732\n",
       " [81]  3.085187747  1.722440703  0.445838206  3.266576538  4.105689740\n",
       " [86]  1.336297201  4.055080791  1.765905851  3.591423519  2.463207191\n",
       " [91]  0.012264115  3.268167726  0.385862768  3.178868897  0.920671530\n",
       " [96]  1.341127136  0.060327433  2.979727949  3.784386473  0.993724382"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rexp(n=100, rate=.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Weibull Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T11:50:11.820751Z",
     "iopub.status.busy": "2022-04-26T11:50:11.819575Z",
     "iopub.status.idle": "2022-04-26T11:50:11.832390Z",
     "shell.execute_reply": "2022-04-26T11:50:11.831131Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
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       "1. 4499.9469087383\n",
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       "99. 5725.83423782393\n",
       "100. 5672.22971901444\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  [1]  4499.9469  4042.5563  1073.1496  3159.0999  4974.5261  2949.6250\n",
       "  [7]  2128.0114  2405.7802  1436.2068   990.8704 15948.7863  2193.5512\n",
       " [13]   431.2380  8021.5171  7176.8527  1726.1685 15432.2320  3722.5258\n",
       " [19]  2315.5834  4688.6165  5773.7101  5957.3862  4420.9181 11118.2133\n",
       " [25]  5644.0183   268.1725  3278.2946  5831.1883  1897.1073  2874.1405\n",
       " [31]  3694.6321  6936.2837 11993.7819  2089.0115 11197.4556  8322.2591\n",
       " [37]  2814.7802   814.7315 10274.4828  2555.7808  3194.2294  5561.8328\n",
       " [43]  5051.0215  2202.9072  1804.1324  2940.9301  9353.6981 10680.6408\n",
       " [49] 14120.9182  4105.9855  4906.5105  6699.0250  3972.1596  8777.2478\n",
       " [55]  4070.6581   402.4620  1870.7039  4313.7891    72.8319  8042.1638\n",
       " [61]  2897.0133  4862.7379  6869.3911  6005.3425  3371.3165  3218.0901\n",
       " [67]   998.1284   757.3426  2220.9315   275.2842  4895.8063  8644.0165\n",
       " [73]   762.5403  3827.4317  1314.1232   874.4762   564.9984  6972.1248\n",
       " [79]  4515.3303  4234.6136  7463.3809  1168.3263  2127.9401  3922.4539\n",
       " [85] 15338.5370  3636.3710  4700.7371  3738.2289  3649.2965  3075.8736\n",
       " [91]  4767.1117  7382.9251  1862.7404  1723.9324  5358.5367  3783.5527\n",
       " [97]  1631.6235  9452.3934  5725.8342  5672.2297"
      ]
     },
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     "output_type": "display_data"
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   ],
   "source": [
    "rweibull(100, 1.5, 5000)"
   ]
  }
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